(CNN) -- A key portion of former FBI Deputy Director Andrew McCabe's testimony to the House Intelligence Committee has served as the backbone for a controversial memo propped up by Republican lawmakers, but McCabe now tells CNN that House Republicans twisted his answers.

The highly controversial memo from Committee Chairman Devin Nunes claimed McCabe testified that "no surveillance warrant would have been sought" for a Trump campaign aide without a disputed opposition-research dossier on Trump and Russia. Not so says McCabe -- the former No. 2 official at the FBI who signed one of the applications to surveil former Trump campaign foreign policy adviser Carter Page.

"We started the investigations without the dossier. We were proceeding with the investigations before we ever received that information," McCabe told CNN as part of a wide-ranging interview. "Was the dossier material important to the package? Of course, it was. As was every fact included in that package. Was it the majority of what was in the package? Absolutely not."

McCabe was fired Friday, less than two days shy of his official retirement.

Some Republicans lawmakers have attempted to cast the dossier as an inherently unreliable piece of opposition research because it was funded through the Democratic National Committee and Hillary Clinton campaign, but McCabe says his testimony was "selectively quoted" and "mischaracterized" in order to bolster the claim that the dossier served as the essential linchpin to the surveillance warrant on Page.

Yet Republicans have stood by their characterization of the dossier's role in the FISA memo. "The dossier formed 'a significant portion' of the Carter Page FISA application," House Intelligence Committee Republicans say in a rebuttal to the Democratic House Intelligence Committee counter-memo.

Democrats, however, have resoundingly rejected the Nunes memo as an inaccurate and misleading portrait intended to distract from Special Counsel Robert Mueller's Russia probe. But McCabe had not gone on record disputing House Republicans' characterization of his testimony until now. He appeared for more than 16 hours of testimony behind closed doors in two sessions in December before members of the House Intelligence, Oversight and Judiciary committees, amid repeated calls for his firing from President Donald Trump and Republicans critical of the FBI's handling of both the Clinton email-server probe and the Russia investigation.